A farmer sell his two cows. On one, he gains 25% and on the other, he losses 25%. Find his gain or loss percent in whole transaction.

Options

A. 6.25% profit
B. 6.25% loss
C. Neither profit nor loss
D. None of the above

Answer

To find the overall gain or loss percentage when a farmer sells two cows, one at a gain of 25% and the other at a loss of 25%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Selling Prices**:
- Let the cost price of the first cow be \( CP_1 \).
- Let the cost price of the second cow be \( CP_2 \).

2. **Calculate Selling Price of the First Cow**:
- The farmer gains 25% on the first cow.
- Selling Price (SP) of the first cow:
\[ SP_1 = CP_1 + 0.25 \times CP_1 = 1.25 \times CP_1 \]

3. **Calculate Selling Price of the Second Cow**:
- The farmer loses 25% on the second cow.
- Selling Price (SP) of the second cow:
\[ SP_2 = CP_2 - 0.25 \times CP_2 = 0.75 \times CP_2 \]

4. **Total Cost Price**:
- Total Cost Price (CP) of both cows:
\[ Total\ CP = CP_1 + CP_2 \]

5. **Total Selling Price**:
- Total Selling Price (SP) of both cows:
\[ Total\ SP = SP_1 + SP_2 = 1.25 \times CP_1 + 0.75 \times CP_2 \]

6. **Calculate Overall Gain or Loss**:
- To find the overall gain or loss, we need to compare the total selling price with the total cost price.
- Gain or Loss = Total SP - Total CP
- If Total SP < Total CP, then it is a loss.

7. **Using the Formula for Loss Percentage**:
- Since we know that the gain on one cow is equal to the loss on the other cow, we can use the formula for loss percentage:
\[ Loss\% = \frac{Loss}{Total\ CP} \times 100 \]
- Here, the loss can be calculated as:
\[ Loss = \frac{(25^2)}{100} = \frac{625}{100} = 6.25\% \]

### Conclusion:
The overall transaction results in a loss of 6.25%.